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许光映, 王晋宝, 薛大文. 短脉冲激光加热分数阶导热及其热应力研究[J]. 力学学报, 2020, 52(2): 491-502. DOI: 10.6052/0459-1879-19-331
引用本文: 许光映, 王晋宝, 薛大文. 短脉冲激光加热分数阶导热及其热应力研究[J]. 力学学报, 2020, 52(2): 491-502. DOI: 10.6052/0459-1879-19-331
Xu Guangyin, Wang Jinbao, Xue Dawen. INVESTIGATIONS ON THE THERMAL BEHAVIOR AND ASSOCIATED THERMAL STRESSES OF THE FRACTIONAL HEAT CONDUCTION FOR SHORT PULSE LASER HEATING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 491-502. DOI: 10.6052/0459-1879-19-331
Citation: Xu Guangyin, Wang Jinbao, Xue Dawen. INVESTIGATIONS ON THE THERMAL BEHAVIOR AND ASSOCIATED THERMAL STRESSES OF THE FRACTIONAL HEAT CONDUCTION FOR SHORT PULSE LASER HEATING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 491-502. DOI: 10.6052/0459-1879-19-331

短脉冲激光加热分数阶导热及其热应力研究

INVESTIGATIONS ON THE THERMAL BEHAVIOR AND ASSOCIATED THERMAL STRESSES OF THE FRACTIONAL HEAT CONDUCTION FOR SHORT PULSE LASER HEATING

  • 摘要: 短脉冲激光加热引起材料内部复杂的传热过程及热变形,现有的以Fourier定律或Cattaneo-Vernotte松弛方程结合弹性理论为框架建立起来热应力理论在刻画其热物理过程存在严重缺陷. 本文基于分数阶微积分理论, 以半空间为研究对象, 建立了分数阶Cattaneo热传导方程和相应的热应力方程, 给出了问题的初始条件和边界条件, 采用拉普拉斯变换方法, 给出了非高斯时间分布激光热源辐射下温度场和热应力场的解析解, 研究了短脉冲激光加热的温度场及热应力场的热物理行为. 数值计算中, 首先对理论解进行数值验证, 然后取分数阶变量p=0.5研究温度场和热应力场的变化特点及激光参数对温度和热应力的影响,最后数值计算分数阶参数对温度和热应力场的影响. 计算结果表明, 分数阶Cattaneo传热方程和热应力方程描述的温度和热应力任然具有波动特性,与经典的Fourier传热模型和标准的Cattaneo传热模型相比, 分数阶阶次越大, 热波波速越小, 热波波动性越明显; 反之, 则热波波速越大, 热扩散性越强.激光加热和冷却的速度越快, 温度上升和下降的速度越快, 压应力和拉应力交替变化越快, 温度变化幅值越小, 热应力幅值影响不明显.

     

    Abstract: For complex heat transfer process and related thermal stress in materials subjected to short pulse laser heating, the existing thermal stress theory based on Fourier law or Cattaneo-Vernotte relaxation equation combined with elastic theory has serious defects in describing its thermophysical process.In this paper, based on the fractional calculus theory, the fractional Cattaneo type heat conduction equation and the corresponding thermal stress equation with appropriate initial and boundary conditions are established for a semi-infinite space irradiated by non-Gaussian lase. The analytical solutions of the temperature field and the thermal stress field are obtained via Laplace transform method, and the thermophysical behaviors are illustrated. Firstly, the theoretical solution is verified, then the variations of temperature field and thermal stress field are studied under the fractional order p=0.5, and the influence of laser parameters on temperature and thermal stress field are also researched. Finally, the effects of fractional order parameters on temperature and thermal stress field are calculated. The calculation results show that the temperature and thermal stress fields described by the fractional Cattaneo type heat transfer equation and thermal stress equation have wave diffusion the characteristics. Compared with the classical Fourier heat transfer model and the standard Cattaneo type heat transfer model, the larger the fractional order is, the smaller the thermal wave velocity is, the more significant the thermal wave dynamics is. On the contrary, the larger the thermal wave velocity is, the stronger the thermal diffusivity is. The faster the laser heating and cooling rate is, the faster the temperature rises and falls, the faster the alternating change of compressive stress and tensile stress is, the smaller the temperature change amplitude is, and the variations of thermal stress amplitude is not obvious

     

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